pymor.models.interface

Module Contents

Classes

Model

Interface for model objects.

class pymor.models.interface.Model(products=None, error_estimator=None, visualizer=None, name=None)

Bases: pymor.core.cache.CacheableObject, pymor.parameters.base.ParametricObject

Interface for model objects.

A model object defines a discrete problem via its class and the Operators it contains. Furthermore, models can be solved for given parameter values resulting in a solution VectorArray.

solution_space

VectorSpace of the solution VectorArrays returned by solve.

dim_output

Dimension of the model output returned by output. 0 if the model has no output.

linear

True if the model describes a linear problem.

products

Dict of inner product operators associated with the model.

_compute_allowed_kwargs

_compute(self, solution=False, output=False, solution_d_mu=False, output_d_mu=False, solution_error_estimate=False, output_error_estimate=False, output_d_mu_return_array=False, mu=None, **kwargs)

abstract _compute_solution(self, mu=None, **kwargs)

Compute the model’s solution for parameter values mu.

This method is called by the default implementation of compute in pymor.models.interface.Model.

Parameters

mu

Parameter values for which to compute the solution.

kwargs

Additional keyword arguments to customize how the solution is computed or to select additional data to be returned.

Returns

VectorArray with the computed solution or a dict which at least must contain the key 'solution'.

_compute_output(self, solution, mu=None, **kwargs)

Compute the model’s output for parameter values mu.

This method is called by the default implementation of compute in pymor.models.interface.Model. The assumption is made that the output is a derived quantity from the model’s internal state as returned my _compute_solution. When this is not the case, the computation of the output should be implemented in _compute.

Note

The default implementation applies the Operator given by the output_functional attribute to the given solution VectorArray.

Parameters

solution

Internal model state for the given parameter values.

mu

Parameter values for which to compute the output.

kwargs

Additional keyword arguments to customize how the output is computed or to select additional data to be returned.

Returns

NumPy array with the computed output or a dict which at least must contain the key 'output'.

abstract _compute_solution_d_mu_single_direction(self, parameter, index, solution, mu=None, **kwargs)

Compute the partial derivative of the solution w.r.t. a parameter index

Parameters

parameter

parameter for which to compute the sensitivity

index

parameter index for which to compute the sensitivity

solution

Internal model state for the given Parameter value.

mu

Parameter value for which to solve

Returns

The sensitivity of the solution as a VectorArray.

_compute_solution_d_mu(self, solution, mu=None, **kwargs)

Compute all partial derivative of the solution w.r.t. a parameter index

Parameters

solution

Internal model state for the given Parameter value.

mu

Parameter value for which to solve

Returns

A dict of all partial sensitivities of the solution.

_compute_output_d_mu(self, solution, mu=None, return_array=False, **kwargs)

Compute the gradient w.r.t. the parameter of the output functional

Parameters

solution

Internal model state for the given Parameter value.

mu

Parameter value for which to compute the gradient

return_array

if True, return the output gradient as a NumPy array. Otherwise, return a dict of gradients for each Parameter.

Returns

The gradient as a NumPy array or a dict of NumPy arrays.

_compute_solution_error_estimate(self, solution, mu=None, **kwargs)

Compute an error estimate for the computed internal state.

This method is called by the default implementation of compute in pymor.models.interface.Model. The assumption is made that the error estimate is a derived quantity from the model’s internal state as returned my _compute_solution. When this is not the case, the computation of the error estimate should be implemented in _compute.

Note

The default implementation calls the estimate_error method of the object given by the error_estimator attribute, passing solution, mu, self and **kwargs.

Parameters

solution

Internal model state for the given parameter values.

mu

Parameter values for which to compute the error estimate.

kwargs

Additional keyword arguments to customize how the error estimate is computed or to select additional data to be returned.

Returns

The computed error estimate or a dict which at least must contain the key 'solution_error_estimate'.

_compute_output_error_estimate(self, solution, mu=None, **kwargs)

Compute an error estimate for the computed model output.

This method is called by the default implementation of compute in pymor.models.interface.Model. The assumption is made that the error estimate is a derived quantity from the model’s internal state as returned my _compute_solution. When this is not the case, the computation of the error estimate should be implemented in _compute.

Note

The default implementation calls the estimate_output_error method of the object given by the error_estimator attribute, passing solution, mu, self and **kwargs.

Parameters

solution

Internal model state for the given parameter values.

mu

Parameter values for which to compute the error estimate.

kwargs

Additional keyword arguments to customize how the error estimate is computed or to select additional data to be returned.

Returns

The computed error estimate or a dict which at least must contain the key 'solution_error_estimate'.

compute(self, solution=False, output=False, solution_d_mu=False, output_d_mu=False, solution_error_estimate=False, output_error_estimate=False, output_d_mu_return_array=False, *, mu=None, **kwargs)

Compute the solution of the model and associated quantities.

This methods computes the output of the model it’s internal state and various associated quantities for given parameter values mu.

Note

The default implementation defers the actual computations to the methods _compute_solution, _compute_output, _compute_solution_error_estimate and _compute_output_error_estimate. The call to _compute_solution is cached. In addition, Model implementors may implement _compute to simultaneously compute multiple values in an optimized way. The corresponding _compute_XXX methods will not be called for values already returned by _compute.

Parameters

solution

If True, return the model’s internal state.

output

If True, return the model output.

solution_d_mu

If not False, either True to return the derivative of the model’s internal state w.r.t. all parameter components or a tuple (parameter, index) to return the derivative of a single parameter component.

output_d_mu

If True, return the gradient of the model output w.r.t. the Parameter.

solution_error_estimate

If True, return an error estimate for the computed internal state.

output_error_estimate

If True, return an error estimate for the computed output.

output_d_mu_return_array

if True, return the output gradient as a NumPy array. Otherwise, return a dict of gradients for each Parameter.

mu

Parameter values for which to compute the values.

kwargs

Further keyword arguments to select further quantities that sould be returned or to customize how the values are computed.

Returns

A dict with the computed values.

solve(self, mu=None, return_error_estimate=False, **kwargs)

Solve the discrete problem for the parameter values mu.

This method returns a VectorArray with a internal state representation of the model’s solution for given parameter values. It is a convenience wrapper around compute.

The result may be cached in case caching has been activated for the given model.

Parameters

mu

Parameter values for which to solve.

return_error_estimate

If True, also return an error estimate for the computed solution.

kwargs

Additional keyword arguments passed to compute that might affect how the solution is computed.

Returns

The solution VectorArray. When return_error_estimate is True, the estimate is returned as second value.

output(self, mu=None, return_error_estimate=False, **kwargs)

Return the model output for given parameter values mu.

This method is a convenience wrapper around compute.

Parameters

mu

Parameter values for which to compute the output.

return_error_estimate

If True, also return an error estimate for the computed output.

kwargs

Additional keyword arguments passed to compute that might affect how the solution is computed.

Returns

The computed model output as a 2D NumPy array. The dimension of axis 1 is : attr:dim_output. (For stationary problems, axis 0 has dimension 1. For time-dependent problems, the dimension of axis 0 depends on the number of time steps.) When return_error_estimate is True, the estimate is returned as second value.

solve_d_mu(self, parameter, index, mu=None, **kwargs)

Solve for the partial derivative of the solution w.r.t. a parameter index

Parameters

parameter

parameter for which to compute the sensitivity

index

parameter index for which to compute the sensitivity

mu

Parameter value for which to solve

Returns

The sensitivity of the solution as a VectorArray.

output_d_mu(self, mu=None, return_array=False, **kwargs)

Compute the gradient w.r.t. the parameter of the output functional.

Parameters

mu

Parameter value for which to compute the gradient

return_array

if True, return the output gradient as a NumPy array. Otherwise, return a dict of gradients for each Parameter.

Returns

The gradient as a NumPy array or a dict of NumPy arrays.

estimate_error(self, mu=None, **kwargs)

Estimate the error for the computed internal state.

For given parameter values mu this method returns an error estimate for the computed internal model state as returned by solve. It is a convenience wrapper around compute.

The model error could be the error w.r.t. the analytical solution of the given problem or the model reduction error w.r.t. a corresponding high-dimensional Model.

Parameters

mu

Parameter values for which to estimate the error.

kwargs

Additional keyword arguments passed to compute that might affect how the error estimate (or the solution) is computed.

Returns

The estimated error.

estimate_output_error(self, mu=None, **kwargs)

Estimate the error for the computed output.

For given parameter values mu this method returns an error estimate for the computed model output as returned by output. It is a convenience wrapper around compute.

The output error could be the error w.r.t. the analytical solution of the given problem or the model reduction error w.r.t. a corresponding high-dimensional Model.

Parameters

mu

Parameter values for which to estimate the error.

kwargs

Additional keyword arguments passed to compute that might affect how the error estimate (or the output) is computed.

Returns

The estimated error.

visualize(self, U, **kwargs)

Visualize a VectorArray U of the model’s solution_space.

Parameters

U

The VectorArray from solution_space that shall be visualized.

kwargs

Additional keyword arguments to customize the visualization. See the docstring of self.visualizer.visualize.